Pascal triangles are formulated for computing the coefficients of the B-spline series representation of the compactly supported spline-wavelets with minimum support and their derivatives.It is shown that with the al- ...Pascal triangles are formulated for computing the coefficients of the B-spline series representation of the compactly supported spline-wavelets with minimum support and their derivatives.It is shown that with the al- ternating signs removed,all these sequences are totally positive.On the other hand,truncations of the recipro- cal Euler-Frobenius polynomials lead to finite sequences for orthogonal wavelet decompositions.For this pur- pose,sharp estimates are given in terms of the exact reconstruction of these approximate decomposed compo- nents.展开更多
基金Research supported by NSF Grant DMS 89-0-01345 and ARO Contract No.DAAL 03-90-G-0091.
文摘Pascal triangles are formulated for computing the coefficients of the B-spline series representation of the compactly supported spline-wavelets with minimum support and their derivatives.It is shown that with the al- ternating signs removed,all these sequences are totally positive.On the other hand,truncations of the recipro- cal Euler-Frobenius polynomials lead to finite sequences for orthogonal wavelet decompositions.For this pur- pose,sharp estimates are given in terms of the exact reconstruction of these approximate decomposed compo- nents.
